# On Weak Integer Additive Set-Indexers of Certain Graph Classes

Source: [On Weak Integer Additive Set-Indexers of Certain Graph Classes](<https://www.sota2.com/research/paper/68fa51bb1e209131ce975ef9>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:55:35.162Z

Authors: N. K. Sudev, K. A. Germina

Published: 2014-02-27T18:58:58.000Z

## Abstract

An integer additive set-indexer is defined as an injective function $f:V(G)\\rightarrow 2^{\\mathbb{N}\_0}$ such that the induced function $g\_f:E(G) \\rightarrow 2^{\\mathbb{N}\_0}$ defined by $g\_f (uv) = f(u)+ f(v)$ is also injective. An integer additive set-indexer is said to be $k$-uniform if $\|g\_f(uv)\|=k$ for all $u,v\\in V(G)$. An integer additive set-indexer $f$ is said to be a weak IASI if $\|g\_f(uv)\|=max(\|f(u)\|,\|f(v)\|)$ for all $u,v\\in V(G)$. The sparing number of a graph $G$ is the minimum number of edges in $G$ with singleton set-labels, so that $G$ admits a weak integer additive set-indexer. In this paper, we study the admissibility of weak integer additive set-indexers by certain graph classes and certain associated graphs of given graphs.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1402.7020>)

[PDF](<https://arxiv.org/pdf/1402.7020.pdf>)